I tried the dish towel and iron idea (brilliant!). It was looking good, about 85% to 90% of the original look. But, not as good as I hoped, so I raised the temperature just to where I noticed the very slightest shallow rolls in the clear window at the edge of melting I suppose. Then, I backed it off a bit. Several passes, and different heating times did not make much difference.
Then, after it cooled, I accidentally caught a corner with my hand and a large section just popped up again
More of the clear layer has released with the heat treatment. Then, I pulled just a bit too much a few tiny paint patches have lifted now.
So, on the edge of a lost cause, I'm trying 3M 77 contact cement. Covered the front surface and window with blue painters tape, sprayed on the contact cement, and it's out drying in the sun with a weight on top. Maybe it will look passable until someday when I can pick up a late model DOA parts unit for something like $35 for a replacement front panel.
As an aside, some of those round calibration tags are agony to remove even with solvents, without scratching the front panel. However, after a few seconds of steam iron, one lifted right off the short front panel calibration cover, intact!
(some sort of optical cement, as mentioned earlier, might have worked. not sure how difficult it would have been to keep it from marking the window)